The invention relates to improvements in two-wavelength phase-shifting interferometry, and more particularly, to improvements which make possible the obtaining of single-wavelength precision in interferometric measurements with the dynamic range of two-wavelength interferometric measurements, and application thereof to testing aspheric surfaces.
Two-wavelength holography and phase-shifting interferometry are known techniques for nondestructively testing optical surfaces. Numerous phase-shifting interferometry techniques and apparatus are known, wherein the phase of a wavefront is determined using a single wavelength with very high measurement precision. One such system is described in copending application Ser. No. 6/781,261, filed Sept. 27, 1985, now U.S. Pat. No. 4,639,139, issued Jan. 27, 1987 by inventors Wyant & Prettyjohns, entitled "Optical Profiler Using Improved Phase-shifting Interferometry", and incorporated herein by reference. The single-wavelength phase-shifting interferometry techniques, wherein computers are utilized to record data, compute and subtract surface errors, and compute surface height variations in the measured surface from correct phase data, are fast, require no intermediate recording step, as is required in two-wavelength holography, and avoid the inconvenience of using photographic chemicals.
Two-wavelength phase-shifting interferometry is a recent technique that extends the measurement range of single-wavelength phase-shifting interferometry, allowing the measurement of the profiles of deeper surfaces than has been previously possible with single-wavelength phase-shifting interferometry. The two-wavelength phase-shifting interferometry techniques were derived by applying phase measurement techniques, in place of intermediate recording steps wherein interference patterns were recorded on photographic film, developed, and then illuminated from the same surface with a different wavelength source, producing interference patterns referred to as MOIRE patterns, the phases of which were computed by a computer. This technique represents the closest prior art to the present invention, and is described in detail in "Two-Wavelength Phase-Shifting Interferometry", by Y. Cheng and co-inventor Wyant, "Applied Optics", Volume 23, No. 24, page 4539, Dec. 15, 1984.
The overall state-of-the-art in interferometric optical testing is well presented in the article "Recent Advances in Interferometric Optical Testing", Laser Focus/Electro-Optics, November 1985, page 118 to 132, by co-inventors Wyant and Creath, incorporated herein by reference.
As pointed out in the above-mentioned Cheng and Wyant paper that introduces the concept of two-wavelength phase-shifting interferometry, ordinary single-wavelength phase-shifting interferometry provides very high precision in the range from .lambda./100 .lambda./1000, peak-to-valley. In phase-shifting interferometry, the phase distribution across the interferogram is measured "modulo 2.pi.". In other words, the measured phase distribution will contain 2.pi. discontinuities, which can only be eliminated as long as the slope of the wavefront being measured is small enough that the phase changes by less than .pi. between adjacent detectors or pixels of the detector array. If the latter condition is met, the phase discontinuities can be removed by adding or subtracting 2.pi. to the measured phase until the resulting phase difference between adjacent pixels is always less than .pi..
Unfortunately, it is frequently desirable to be able to test surfaces that are so steep that the measured phase change between adjacent pixels will be greater than .pi., and the 2.pi. ambiguities cannot be eliminated by simple addition or subtraction.
In the Cheng and Wyant paper, a technique for solving the 2.pi. ambiguity problem is introduced, wherein two sets of phase data, with 2.pi. ambiguities present, are stored in a computer, which then calculates the phase difference between pixels for a longer "equivalent" wavelength .lambda..sub.eq. The paper describes an algorithm for computing the phase, wherein an elaborate mathematical summation is performed wherein the difference in phase computed at each of the two-wavelengths is computed for each pixel element, multiplied by a certain number, and the differences between the computed differences for successively adjacent pixels are summed. The problem with that technique is that errors in the computed differences for various pixels also are summed. As a practical matter, the technique described in the Cheng and Wyant paper is much less accurate than is desired, and requires far more computation time than is desirable, even though the technique represents an advance over the two-wavelength holographic techniques of the prior art, because the recording of an interferogram on film is not required, and the alignment problems associated with two-wavelength holography are avoided. In the technique of the Cheng and Wyant paper, the pixel errors increase with approximately the square root of the number of detector points in the detector array, and certain arithmetic round-off errors and electronic noise associated with the detector elements are cumulatively summed over the entire detector array. As a result, in applications wherein two-wavelength phase-shifting interferometry might be advantageous without the above-mentioned problems, such as in testing certain aspheric surfaces, it often will be necessary to instead rely on prior techniques for measuring of contouring aspheric surfaces.
Up to now, phase-shifting interferometric techniques that utilize longer equivalent wavelengths have resulted in a substantial loss of accuracy and, as a practical matter, have not been applicable to measurement of many aspheric surfaces.
Those skilled in the art recognize that economical, accurate measuring of aspheric optical components has been an important objective in the optics art. Those skilled in the art know that most optical surfaces presently are spherical surfaces. However, if it were possible to make economical aspheric surfaces, better optical performance often could be obtained. Optical systems designed with aspheric optical components may be lighter in weight, have fewer elements, and therefore have the potential for being less expensive. Designing aspheric optical components is not a major problem, as computer software for so doing has been available for quite some time. Up to now, however, fabrication of aspheric optical components has been very expensive, because there has been no inexpensive, practical means of testing them.
One prior technique for testing aspheric surfaces has been to utilize "null lenses" wherein an aspheric optical component is fabricated that exactly cancels the asphericity in the optical element being tested. Unfortunately, the aspheric null lens has to be manufactured first, using testing techniques that are very expensive. For every new optical aspheric component that is to be constructed, a separate expensive null lens must be manufactured, usually for that purpose only.
Typically, the null lens is manufactured and tested by techniques that require many spherical components precisely assembled in a manner known to those skilled in the art. Providing such an assembly of spherical lenses to test aspheric elements is known to be a difficult undertaking.
For many years, co-inventor Wyant has worked on producing computer-generated holograms that each can be used for testing a certain aspheric element of an optical system. This technique has worked, but it has been expensive and difficult because a new hologram is needed for every asphere to be tested. In order to make a single hologram, an expensive, high precision plotting device is required, and many hours are required to plot a single hologram. The prior art for testing aspheric optical components frequently involves set up costs of tens of thousands of dollars for each new aspheric optical element to be tested.
There is a substantial unmet need for a technique of improving the accuracy of two-wavelength phase-shifting interferometry to increase accuracy and reduce speed of computation.
There also is a great unmet need for an inexpensive, improved technique of testing steep aspheric surfaces without the use of null lens and holograms.
There is also a great unmet need for an improved technique of testing steep aspheric surfaces with a single test system, and for reducing the time required to test each aspheric surface.
A problem that has existed in prior phase-shifting interferometers at the present state-of-the-art has been that of operating on data stored in a computer to correct data errors produced by various sources, such as stray reflections and scattered light. Prior techniques have included the technique of determining the intensity difference between data frames computed at a single pixel or detector as the phase is shifted, and if the computed difference was too small, eliminating the computed phase. This approach often resulted in discarding good data as well as bad because the phases may have been computed from intensity measurements at points that are near a peak or valley of a fringe where the intensity does not change much between consecutive measurements.